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A framework is established for evaluating {\sc cphase} gates that usesingle-photon cross-phase modulation (XPM) originating from the Kerrnonlinearity. Prior work Phys. Rev. A {\bf 73,} 062305 (2006)], which assumedthat the control and target pulses propagated at the same group velocity,showed that the causality-induced phase noise required by a non-instantaneousXPM response function precluded the possibility of high-fidelity $\pi$-radianconditional phase shifts. The framework presented herein incorporates the morerealistic case of group-velocity disparity between the control and targetpulses, as employed in existing XPM-based fiber-optical switches. Nevertheless,the causality-induced phase noise identified in [Phys. Rev. A {\bf 73,} 062305(2006)] still rules out high-fidelity $\pi$-radian conditional phase shifts.This is shown to be so for both a reasonable theoretical model for the XPMresponse function and for the experimentally-measured XPM response function ofsilica-core fiber.

Phase-noise limitations on single-photon cross-phase modulation with differing group velocities